Algebra 1: Quadratic Functions Review (Ch. 9 part 1)
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1 Name: Class: Date: ID: A Algebra 1: Quadratic Functions Review (Ch. 9 part 1) 1. Find the rule of a parabola that has the Ê 1 x-intercepts at ( 6,0) and,0 ˆ 3 ËÁ Find the rule of a parabola that has the x-intercepts at (4,0) and Ê ËÁ 5,0 ˆ. 3. What two lines make up the parabola y = x x What two lines make up the parabola 5. y = 3x 2 + 2x : I can identify the anatomy (vertex, axis of symmetry, min/max) of a parabola and state domain and range. For each of the following quadratic functions state: whether it is a min or a max, the vertex, the axis of symmetry, domain and the range. 7. y = 8x y = 1 5 x y = 1 2 x y = 10x : I can graph quadratic functions of the form y = ax 2 and y = ax 2 + c 11. Graph y = x
2 Name: ID: A 12. Graph y = 2x Identify the vertex, axis of symmetry, domain, range of the graph of the function. Also state whether the function is a min or max, wide/normal,skinny. y = (x 3) Identify the vertex, axis of symmetry, domain, range of the graph of the function. Also state whether the function is a min or max, wide/normal,skinny. y = 3(x + 2) Graph the following function: y = 2(x 4) Put questions 7-12 in order from widest to skinnest. S.Q.1: I can graph, state domain and range, and identify the anatomy of quadratic functions of the form y = a(x h) 2 + k and state domain and range. 14. How is the graph of y = 4x different from the graph of y = 4x 2? a. It is shifted 1 unit(s) up. b. It is shifted 1 unit(s) down. c. It is shifted 1 unit(s) left. d. It is shifted 1 unit(s) right. 20. Graph the following function: y = 1 2 (x + 3) How is the graph of y = 2x 2 5 different from the graph of y = 2x 2? a. It is shifted 5 unit(s) up. b. It is shifted 5 unit(s) down. c. It is shifted 5 unit(s) left. d. It is shifted 5 unit(s) right. 16. Identify the vertex, axis of symmetry, domain, range of the graph of the function. Also state whether the function is a min or max, wide/normal,skinny. y = 2(x + 2)
3 Name: ID: A 9.2.1: I can graph, state domain and range, and identify the anatomy of quadratic functions of the form y = ax 2 + bx + c. 21. State whether the following function is a min/max, wide/normal/skinny, find the vertes, find the axis of symmetry, find domain, and find range. f(x) = x 2 + 2x State whether the following function is a min/max, wide/normal/skinny, find the vertes, find the axis of symmetry, find domain, and find range. f(x) = 4x 2 + 4x f(x) = x 2 + 4x A ball is thrown into the air with an upward velocity of 28 ft/s. Its height h in feet after t seconds is given by the function h = 16t t + 7. How long does it take the ball to reach its maximum height? What is the ball s maximum height? Round to the nearest hundredth, if necessary. 26. A catapult launches a boulder with an upward velocity of 148 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h = 16t t How long does it take the boulder to reach its maximum height? What is the boulder s maximum height? Round to the nearest hundredth, if necessary. S.Q.2: I can model quadratic functions. What is the equation, in standard form, of a parabola that models the values in the table? 27. x f(x) x f(x) = 2x 2 + 2x 1 f(x)
4 Name: ID: A 29. A biologist took a count of the number of migrating at a particular lake, and recounted the lake s population of on each of the next six weeks. Week Population ,070 1,317 Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of at the lake on week 8. a. P(x) = 25x 2 28x + 585; 1,614 b. P(x) = 30x x + 535; 2,679 c. P(x) = 25x 2 28x + 585; 1,961 d. P(x) = 30x x + 535; 2, A biologist took a count of the number of fish in a particular lake, and recounted the lake s population of fish on each of the next six weeks. Week Population Find a quadratic function that models the data as a function of x, the number of weeks. Use the model to estimate the number of fish at the lake on week 11. a. P(x) = 5x 2 17x + 495; 1,842 fish c. P(x) = 10x x + 445; 1,842 fish b. P(x) = 5x 2 17x + 495; 621 fish d. P(x) = 10x x + 445; 1,054 fish 4
5 ID: A Algebra 1: Quadratic Functions Review (Ch. 9 part 1) Answer Section 1. f 2. f 3. f 4. f 5. (0, 1); maximum 6. (0, 2); minimum 7. f 8. f 9. f 10. f 11. f 12. f 13. f 14. A 15. B 16. vertex: ( 2, 4); axis of symmetry: x = minimum value: 4 domain: all real numbers range: all real numbers vertex: ( 2, 2); axis of symmetry: x = f 20. f 21. axis of symmetry: x = 1 vertex: ( 1, 1) 1
6 ID: A axis of symmetry: x = 0.5 vertex: (0.5, 2) axis of symmetry: x = 2 vertex: ( 2, 3) 2
7 ID: A 24. axis of symmetry: x = 0.5 vertex: (0.5, 0.5) s; ft s; ft 27. y = 4x 2 + 6x y = 4x 2 3x C 30. A 3
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